Question

the heating element of an electric oven is designed to produce 3.9 kw of heat when connected to a 240 - v source. part a what must be the resistance of the element? express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Recall power - resistance - voltage formula

The power formula is $P=\frac{V^{2}}{R}$, where $P$ is power, $V$ is voltage and $R$ is resistance. We need to solve for $R$.

Step2: Rearrange the formula for $R$

Rearranging $P = \frac{V^{2}}{R}$ gives $R=\frac{V^{2}}{P}$.

Step3: Convert power to SI units

The power $P = 3.9\ kW=3900\ W$ and the voltage $V = 240\ V$.

Step4: Substitute values into the formula

$R=\frac{(240)^{2}}{3900}=\frac{57600}{3900}\approx14.77\ \Omega$.

Step5: Round to two significant figures

Rounding $14.77\ \Omega$ to two significant figures gives $R = 15\ \Omega$.

Answer:

$R = 15\ \Omega$